Did you learn about these in the same place, or is it just that you've run across both across various articles, etc.? (A link might help with evaluating the rest of my comment.) There's something odd here. links is consistently giving me more results, but link is the actually documented operator. I can't immediately see what the difference is, and if the extras are valid, though. For the time being, I would trust the link: results more if only because it's what you're "supposed" to be using.
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Su'Aug 19 '12 at 19:46

It's a way to get a feel for it.
Arguably Google would prefer that you do it via their Webmaster Tools, where you'll find it under Traffic->Links to Your Site. The link: operator only shows you a selection of results like site: does. (Mentioned at that previous link.) Webmaster Tools is also a better option for this as it provides some extra information like who links to you most, and how your site gets linked to.

Note that if you do continue using the link: operator, Google recommend using the domain name without the www sub-domain. (They're not the same thing.)

[EDIT]
On further review using a domain I control and so could do a better job filtering, it looks like non-existent search operators, eg links: just get ignored and treated as a literal strings as much as possible. It'd be nice if they popped a warning message about this. But for example, if you do a search for "foo:rottentomatoes.com" you'll see results up top for things like the movie "To Wong Foo…" and the actor John Foo, plus even attempts to figure out if your search was a typo, eg. "Kung Fu Panda" also shows up.